Theorem nfoprab2 6705

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 30-Jul-2012.)

Assertion

Ref	Expression
nfoprab2	|- F/_ y { <. <. x , y >. , z >. | ph }

Proof of Theorem nfoprab2

Dummy variable w is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-oprab 6654	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 2027	. . . 4 |- F/ y E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 2154	. . 3 |- F/ y E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfab 2769	. 2 |- F/_ y { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
5	1, 4	nfcxfr 2762	1 |- F/_ y { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 384   = wceq 1483   E.wex 1704   {cab 2608   F/_wnfc 2751   <.cop 4183   {coprab 6651

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-oprab 6654

This theorem is referenced by:  ssoprab2b  6712  nfmpt22  6723  ov3  6797  tposoprab  7388